Absolute value

2010001604

Level:

Which equation describes real numbers

x

that are equidistant from the numbers

- 2

and

3

on the number line?

| x + 2 | = | x - 3 |

| x + 2 | = | x + 3 |

| x - 2 | = | x - 3 |

| x - 2 | = | x + 3 |

2010001603

Level:

Assuming

x \in (1; 8)

, simplify the following expression.

2 | x - 8 | - 2 | 1 - x |

- 4 x + 18

14

4 x - 18

- 14

2010001602

Level:

Simplifying

| \sqrt{3} - 3 | - | 2 \sqrt{3} - 2 |

we get:

- 3 \sqrt{3} + 5

- 3 \sqrt{3} + 1

\sqrt{3} + 5

\sqrt{3} + 1

2010001601

Level:

Evaluate the following expression.

| 2 - 5 | + | 2 (- 3) | - | (- 3) (- 1) |

6

12

- 12

- 6

2000001605

Level:

Find all

x

such that the statement is true.

| - 1 - x | = 1 + x

x \in [- 1; \infty)

x \in [1; \infty)

x \in [0; \infty)

x \in R

2000001604

Level:

Find all

x

such that the statement is true.

| 3 - 2 x | = - 3 + 2 x

x \in [\frac{3}{2}; \infty)

x \in [2; \infty)

No such

x

exists.

x \in R

2000001603

Level:

Find all

x

such that the statement is true.

| - 1 - x | = - 1 - x

x \in (- \infty; - 1]

x \in (- \infty; 1]

x \in [1; \infty)

No such

x

exists.

2000001602

Level:

Find all

x

such that the statement is true.

| 1 - x | = 1 - x

x \in (- \infty; 1]

x \in [1; \infty)

x \in [- 1; \infty)

x \in (- \infty; - 1]

2000001601

Level:

Find all

x

such that the statement is true.

| 2 x - 1 | = 2 x - 1

x \in [\frac{1}{2}; \infty)

x \in [2; \infty)

x \in [- 2; \infty)

x \in [5; \infty)

2000001315

Level:

Evaluate the given expression.

| 1 - \sqrt{2} | + | 3 - \sqrt{2} |

2

2 \sqrt{2}

\sqrt{2} + 1

2 \sqrt{2} + 4

2010001604

2010001603

2010001602

2010001601

2000001605

2000001604

2000001603

2000001602

2000001601

2000001315

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